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Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei Chinese Quarterly Journal of Mathematics    2025, 40 (3): 304-312.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006 Abstract （157）      PDF（pc） （354KB）（48）       Knowledge map    Save We investigate the blow-up effect of solutions for a non-homogeneous wave equation utt −∆u−∆ut =I0α+ (|u|p)+ω(x), where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent. Related Articles | Metrics

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Moments of Dirichlet L-Functions HUANG Bing-rong, HUANG Jun-hao Chinese Quarterly Journal of Mathematics    2025, 40 (4): 360-371.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.003 Abstract （157）      PDF（pc） （346KB）（60）       Knowledge map    Save In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin. Related Articles | Metrics

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ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces LI Hong-feng, LIU Ke-feng, WANG Yong Chinese Quarterly Journal of Mathematics    2025, 40 (2): 111-134.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.001 Abstract （145）      PDF（pc） （367KB）（48）       Knowledge map    Save In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces. Related Articles | Metrics

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A High-Order Scalar Auxiliary Variable Approach for Nonlinear Parabolic Integro-Differential Equations YAN Li-na, ZHANG Gen-gen, HUANG Qiong-ao Chinese Quarterly Journal of Mathematics    2025, 40 (3): 262-270.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.003 Abstract （129）      PDF（pc） （365KB）（13）       Knowledge map    Save An efficient and accurate scalar auxiliary variable (SAV) scheme for numerically solving nonlinear parabolic integro-differential equation (PIDE) is developed in this paper. The original equation is first transformed into an equivalent system, and the k-order backward differentiation formula (BDFk) and central difference formula are used to discretize the temporal and spatial derivatives, respectively. Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms, the proposed scheme is based on the SAV idea and can be treated semi-implicitly, taking into account both accuracy and effectiveness. Numerical results are presented to demonstrate the high-order convergence (up to fourth-order) of the developed schemes and it is computationally efficient in long-time computations. Related Articles | Metrics

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Applications of Matrix Equations in Linear Time-Invariant Systems ZHOU Yan-ping, CHEN Yan-ping, ZHANG Juan Chinese Quarterly Journal of Mathematics    2025, 40 (3): 221-237.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.001 Abstract （115）      PDF（pc） （337KB）（43）       Knowledge map    Save With the development of science and technology, the design and optimization of control systems are widely applied. This paper focuses on the application of matrix equations in linear time-invariant systems. Taking the inverted pendulum model as an example, the algebraic Riccati equation is used to solve the optimal control problem, and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix. Then, the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems, with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration. Two methods for solving the Lyapunov equations are introduced, providing references for related research. Related Articles | Metrics

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On the Best Constant in Poincar´e Inequality over Simple Geometric Domains CHEN Hong-ru, MA Gao-chao, ZHANG Bei Chinese Quarterly Journal of Mathematics    2025, 40 (2): 148-157.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003 Abstract （112）      PDF（pc） （410KB）（14）       Knowledge map    Save In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain. Related Articles | Metrics

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Numerical Methods for Boundary Value Problems in Variable Coefficient Ordinary Differential Equations ZHAO Ting-ting, CAI Wei-yun Chinese Quarterly Journal of Mathematics    2025, 40 (3): 295-303.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.005 Abstract （106）      PDF（pc） （422KB）（16）       Knowledge map    Save In order to solve the problem of the variable coefficient ordinary differential equation on the bounded domain, the Lagrange interpolation method is used to approximate the exact solution of the equation, and the error between the numerical solution and the exact solution is obtained, and then compared with the error formed by the difference method, it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation. Related Articles | Metrics

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xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2025, 40 (2): 135-147.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.002 Abstract （100）      PDF（pc） （320KB）（19）       Knowledge map    Save The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations (VSIEs) with convolution and Cauchy kernels in a more general function class. To obtain the analytic solutions, we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis. In view of the analytical Riemann-Hilbert method, the generalized Liouville theorem and Sokhotski-Plemelj formula, we get the uniqueness and existence of solutions for such problems, and study the asymptotic property of solutions at nodes. Therefore, this paper improves the theory of singular integral equations and boundary value problems. Related Articles | Metrics

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A Posteriori Error Estimate of Multiphysics Discontinuous Galerkin Method for a Poroelasticity#br# GE Zhi-hao, HE Wen-long, MA Meng-xia Chinese Quarterly Journal of Mathematics    2025, 40 (3): 238-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.002 Abstract （94）      PDF（pc） （1766KB）（13）       Knowledge map    Save In this paper, we design a new error estimator and give a posteriori error analysis for a poroelasticity model. To better overcome “locking phenomenon” on pressure and displacement, we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model. And we prove the upper and lower bound of the proposed error estimators, which are numerically demonstrated to be computationally very efficient. Finally, we present numerical examples to verify and validate the efficiency of the proposed error estimators, which show that the adaptive scheme can overcome “locking phenomenon” and greatly reduce the computation cost. Related Articles | Metrics

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The Gauss Circle Problem Related to the Fourier Coefficients of Cusp Forms CHEN Feng Chinese Quarterly Journal of Mathematics    2025, 40 (3): 313-323.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.007 Abstract （93）      PDF（pc） （363KB）（28）       Knowledge map    Save Let f be a Hecke eigenform of even integral weight k for the full modular group SL2(Z). Denote by λf (n) the nth normalized coefficient of f. The sum of Fourier coefficients of cusp form over the quadratic polynomial m2 +n2 is considered, i.e.,... Related Articles | Metrics

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New Series Involving Binomial Coefficients (III) SUN Zhi-wei Chinese Quarterly Journal of Mathematics    2025, 40 (4): 372-392.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.004 Abstract （86）      PDF（pc） （428KB）（13）       Knowledge map    Save We evaluate some series with summands involving a single binomial coefficien…… Related Articles | Metrics

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On New Generalizations of Hermite-Hadamard Inequalities via (p,q)-Integral LIU Xue, CHENG Li-hua Chinese Quarterly Journal of Mathematics    2025, 40 (2): 211-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.008 Abstract （85）      PDF（pc） （330KB）（27）       Knowledge map    Save This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via (p,q)-quantum integrals. First, based on the definitions of (p,q)-derivatives and integrals over finite intervals, we establish a unified (p,q)-Hermite-Hadamard inequality framework, combining midpoint-type and trapezoidal-type inequalities into a single form. Furthermore, by introducing a parameter λ, we propose a generalized (p,q)-integral inequality, whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature. Furthermore, using hybrid integral techniques, we construct refined inequalities that incorporate (p,q)-integral terms, and by adjusting λ, we demonstrate their improvements and extensions to known inequalities. Specific examples are provided to validate the applicability of the results. The findings indicate that the proposed (p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error, convex optimization problems, and analysis of system performance in control theory, thus enriching the research results of quantum calculus in the field of inequalities. Related Articles | Metrics

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On an Open Problem in Bottleneck Algebra TAN Yi-jia Chinese Quarterly Journal of Mathematics    2025, 40 (3): 324-330.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.008 Abstract （82）      PDF（pc） （292KB）（13）       Knowledge map    Save A bottleneck algebra is a linearly ordered set (B,≤) with two operations a⊕b=max{a,b} and a⊗b=min{a,b}. A finite nonempty set of vectors of order m over a bottleneck algebra B is said to be 2B-independent if each vector of order m over B can be expressed as a linear combination of vectors in this set in at most one way. In 1996, Cechl´arov´a and Pl´avka posed an open problem: Find a necessary and sufficient condition for a finite nonempty set of vectors of order m over B to be 2B-independent. In this paper, we derive some necessary and sufficient conditions for a finite nonempty set of vectors of order m over a bounded bottleneck algebra to be 2B-independent and answer this open problem. Related Articles | Metrics

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The Dynamic Behavior of Asymmetric Large-Scale Ring Neural Network with Multiple Delays ZHANG Wen-yu, LI Ming-hui, CHENG Zun-shui Chinese Quarterly Journal of Mathematics    2025, 40 (2): 169-179.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.005 Abstract （77）      PDF（pc） （4997KB）（11）       Knowledge map    Save The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results. Related Articles | Metrics

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A Survey on Waring’s Problem and Some Related Topics ZHAO Li-lu Chinese Quarterly Journal of Mathematics    2025, 40 (4): 393-400.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.005 Abstract （74）      PDF（pc） （323KB）（16）       Knowledge map    Save The aim of this survey is to introduce Waring’s problem and some related topics including mean value theorems and Diophantine equations in prime variables. Related Articles | Metrics

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Boundedness in Discontinuous Oscillations at Nonresonance BIAN Jing-ke, LIU Jie Chinese Quarterly Journal of Mathematics    2025, 40 (2): 180-202.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.006 Abstract （71）      PDF（pc） （419KB）（9）       Knowledge map    Save In this paper, we first consider a specific discontinuous differential equation for a smooth and discontinuous (SD) oscillator Related Articles | Metrics

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A Note on Strongly Semipotent Rings MENG Yan-mei, GUO Yong-hua Chinese Quarterly Journal of Mathematics    2025, 40 (2): 203-210.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.007 Abstract （70）      PDF（pc） （302KB）（12）       Knowledge map    Save This note is to investigate the properties of strongly semipotent rings. It is proved that every strongly semipotent ring is a idempotent unit regular ring, i.e., there exist a non-zero idempotent e and a unit u such that er =eu for all r /∈J(R), where J(R) is the Jacobson radical of ring R. Related Articles | Metrics

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Optimal Error Estimates of Multiphysics Finite Element Method for a Nonlinear Poroelasticity Model with Nonlinear Stress-Strain Relation GE Zhi-hao, LI Hai-run, LI Ting-ting Chinese Quarterly Journal of Mathematics    2025, 40 (3): 271-294.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.004 Abstract （70）      PDF（pc） （985KB）（10）       Knowledge map    Save In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation. Firstly, we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. Secondly, a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically. Thirdly, existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically. Lastly, numerical tests are given to verify the theoretical results. Related Articles | Metrics

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A Survey on Sumset Problems of Finite Integer Sets TANG Min Chinese Quarterly Journal of Mathematics    2025, 40 (4): 352-359.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.002 Abstract （69）      PDF（pc） （309KB）（17）       Knowledge map    Save Let A be a finite set of integers. For any integer h≥2, let hA and h ∧A be the sets of all sums of h elements of A and all sums of h distinct elements of A, respectively. In this paper, we survey some significant advances in additive combinatorics concerning the size and structure of sumsets of finite integer sets. Related Articles | Metrics

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Perfect Double Roman Domination on Cographs LI Peng, XUE Xin-yi, LONG Yang-jing, LI Xue-bo Chinese Quarterly Journal of Mathematics    2025, 40 (2): 158-168.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.004 Abstract （68）      PDF（pc） （438KB）（10）       Knowledge map    Save Consider a graph G = (V,E). A perfect double Roman dominating function (PDRDF for short) is a function h:V → {0,1,2,3} that satisfies the condition Related Articles | Metrics